A small square loop of side \('a'\) and one turn is placed inside a larger square loop of side \({b}\) and one turn \((b \gg a)\). The two loops are coplanar with thei centres coinciding. If a current \(I\) is passed in the square loop of side \('b',\) then the coefficient of mutual inductance between the two loops is

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Answer & Solution

Correct Answer

(A) \(\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{{a}^{2}}{{b}}\)

Detailed explanation

\({B}=\left[\frac{\mu_{0}}{4 \pi} \frac{{I}}{{b} / 2} \times 2 \sin 45\right] \times 4\)

\(\phi=2 \sqrt{2} \frac{\mu_{0}}{\pi} \frac{{I}}{{b}} \times {a}^{2}\)

\(\therefore {M}=\frac{\phi}{{I}}=\frac{2 \sqrt{2} \mu_{0} {a}^{2}}{\pi {b}}=\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{{a}^{2}}{{b}}\)

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